Bayesian Reliability / Edition 1

Bayesian Reliability / Edition 1

by Michael S. Hamada, Alyson Wilson, C. Shane Reese, Harry Martz
     
 

ISBN-10: 0387779485

ISBN-13: 9780387779485

Pub. Date: 07/10/2008

Publisher: Springer New York

Bayesian Reliability presents modern methods and techniques for analyzing reliability data from a Bayesian perspective. The adoption and application of Bayesian methods in virtually all branches of science and engineering have significantly increased over the past few decades. This increase is largely due to advances in simulation based computational tools for

Overview

Bayesian Reliability presents modern methods and techniques for analyzing reliability data from a Bayesian perspective. The adoption and application of Bayesian methods in virtually all branches of science and engineering have significantly increased over the past few decades. This increase is largely due to advances in simulation based computational tools for implementing Bayesian methods.

Product Details

ISBN-13:
9780387779485
Publisher:
Springer New York
Publication date:
07/10/2008
Series:
Springer Series in Statistics
Edition description:
2008
Pages:
436
Product dimensions:
6.30(w) x 9.30(h) x 1.00(d)

Table of Contents

Preface VII

1 Reliability Concepts 1

1.1 Defining Reliability 1

1.2 Measures of Random Variation 2

1.3 Examples of Reliability Data 10

1.3.1 Bernoulli Success/Failure Data 10

1.3.2 Failure Count Data 10

1.3.3 Lifetime/Failure Time Data 11

1.3.4 Degradation Data 12

1.4 Censoring 13

1.5 Bayesian Reliability Analysis 15

1.6 Related Reading 18

1.7 Exercises for Chapter 1 19

2 Bayesian Inference 21

2.1 Introductory Concepts 21

2.1.1 Maximum Likelihood Estimation 24

2.1.2 Classical Point and Interval Estimation for a Proportion 26

2.2 Fundamentals of Bayesian Inference 27

2.2.1 The Prior Distribution 28

2.2.2 Combining Data with Prior Information 30

2.3 Prediction 35

2.4 The Marginal Distribution of the Data and Bayes' Factors 36

2.5 A Lognormal Example 39

2.6 More on Prior Distributions 46

2.6.1 Noninformative and Diffuse Prior Distributions 46

2.6.2 Conjugate Prior Distributions 47

2.6.3 Informative Prior Distributions 47

2.7 Related Reading 49

2.8 Exercises for Chapter 2 49

3 Advanced Bayesian Modeling and Computational Methods 51

3.1 Introduction to Markov Chain Monte Carlo (MCMC) 51

3.1.1 Metropolis-Hastings Algorithms 52

3.1.2 Gibbs Sampler 60

3.1.3 Output Analysis 64

3.2 Hierarchical Models 68

3.2.1 MCMC Estimation of Hierarchical Model Parameters 71

3.2.2 Inference for Launch Vehicle Probabilities 71

3.3 Empirical Bayes 73

3.4 Goodness of Pit X 76

3.5 Related Reading .I 82

3.6 Exercises for Chapter 3 82

4 Component Reliability 85

4.1 Introduction 85

4.2 Discrete Data Models for Reliability 86

4.2.1 Success/Failure Data 86

4.2.2 Failure Count Data 87

4.3 Failure Time Data Models for Reliability90

4.3.1 Exponential Failure Times 91

4.3.2 Weibull Failure Times 97

4.3.3 Lognormal Failure Times 102

4.3.4 Gamma Failure Times 104

4.3.5 Inverse Gaussian Failure Times 105

4.3.6 Normal Failure Times 106

4.4 Censored Data 107

4.5 Multiple Units and Hierarchical Modeling 111

4.6 Model Selection 116

4.6.1 Bayesian Information Criterion 116

4.6.2 Deviance Information Criterion 117

4.6.3 Akaike Information Criterion 120

4.7 Related Reading 120

4.8 Exercises for Chapter 4 120

5 System Reliability 125

5.1 System Structure 125

5.1.1 Reliability Block Diagrams 126

5.1.2 Structure Functions 126

5.1.3 Minimal Path and Cut Sets 129

5.1.4 Fault Trees 131

5.2 System Analysis 135

5.2.1 Calculating System Reliability 135

5.2.2 Prior Distributions for Systems 138

5.2.3 Fault Trees with Bernoulli Data 141

5.2.4 Fault Trees with Lifetime Data 145

5.2.5 Bayesian Network Models 147

5.2.6 Models for Dependence 155

5.3 Related Reading 158

5.4 Exercises for Chapter 5 159

6 Repairable System Reliability 161

6.1 Introduction 161

6.1.1 Types of Data 162

6.1.2 Characteristics of System Repairs 162

6.2 Renewal Processes 163

6.3 Poisson Processes 165

6.3.1 Homogeneous Poisson Processes (HPPs 167

6.4 Nonhomogeneous Poisson Processes (NHPPs) 170

6.4.1 Power Law Processes (PLPs) 170

6.4.2 Log-Linear Processes 176

6.5 Alternatives to NHPPs 176

6.5.1 Modulated Power Law Processes (MPLPs) 176

6.5.2 Piecewise Exponential Model (PEXP) 179

6.6 Goodness of Fit and Model Selection 180

6.7 Current Reliability and Other Performance Criteria 181

6.7.1 Current Reliability 181

6.7.2 Other Performance Criteria 182

6.8 Multiple-Unit Systems and Hierarchical Modeling 183

6.9 Availability 192

6.9.1 Other Data Types for Availability 194

6.9.2 Complex System Availability 196

6.10 Related Reading 198

6.11 Exercises for Chapter 6 199

7 Regression Models in Reliability 203

7.1 Introduction 203

7.1.1 Covariate Types 204

7.1.2 Covariate Relationships 205

7.2 Logistic Regression Models for Binomial Data 205

7.3 Poisson Regression Models for Count Data 215

7.4 Regression Models for Lifetime Data 221

7.5 Model Selection 228

7.6 Residual Analysis 229

7.7 Accelerated Life Testing 235

7.7.1 Common Accelerating Variables and Relationships 237

7.8 Reliability Improvement Experiments 243

7.9 Other Regression Situations 258

7.10 Related Reading 259

7.11 Exercises for Chapter 7 259

8 Using Degradation Data to Assess Reliability 271

8.1 Introduction 271

8.1.1 Comparison with Lifetime Data 278

8.2 More Complex Degradation Data Models 279

8.2.1 Reliability Function 281

8.3 Diagnostics for Degradation Data Models 283

8.4 Incorporating Covariates 287

8.4.1 Accelerated Degradation Testing 288

8.4.2 Improving Reliability Using Designed Experiments 295

8.5 Destructive Degradation Data 298

8.6 An Alternative Degradation Data Model Using Stochastic Processes 306

8.7 Related Reading 309

8.8 Exercises for Chapter 8 310

9 Planning for Reliability Data Collection 319

9.1 Introduction 319

9.2 Planning Criteria, Optimization, and Implementation 320

9.2.1 Optimization in Planning 321

9.2.2 Implementing the Simulation-Based Framework 323

9.3 Planning for Binomial Data 324

9.4 Planning for Lifetime Data 327

9.5 Planning Accelerated Life Tests 328

9.6 Planning for Degradation Data 330

9.7 Planning for System Reliability Data 331

9.8 Related Reading 339

9.9 Exercises for Chapter 9 339

10 Assurance Testing 343

10.1 Introduction 343

10.1.1 Classical Risk Criteria 345

10.1.2 Average Risk Criteria 345

10.1.3 Posterior Risk Criteria 346

10.2 Binomial Testing 348

10.2.1 Binomial Posterior Consumer's and Producer's Risks 349

10.2.2 Hybrid Risk Criterion 353

10.3 Poisson Testing 354

10.4 Weibull Testing 358

10.4.1 Single Weibull Population Testing 360

10.4.2 Combined Weibull Accelerated/Assurance Testing 364

10.5 Related Reading 368

10.6 Exercises for Chapter 10 369

A Acronyms and Abbreviations 375

B Special Functions and Probability Distributions 377

B.1 Greek Alphabet 377

B.2 Special Functions 377

B.2.1 Beta Function 377

B.2.2 Binomial Coefficient 378

B.2.3 Determinant 378

B.2.4 Factorial 378

B.2.5 Gamma Function 378

B.2.6 Incomplete Beta Function 378

B.2.7 Incomplete Beta Function Ratio 378

B.2.8 Indicator Function 379

B.2.9 Logarithm 379

B.2.10 Lower Incomplete Gamma Function 379

B.2.11 Standard Normal Cumulative Density Function 379

B.2.12 Standard Normal Probability Density Function 379

B.2.13 Trace 379

B.2.14 Upper Incomplete Gamma Function 379

B.3 Probability Distributions 380

B.3.1 Bernoulli 380

B.3.2 Beta 380

B.3.3 Binomial 382

B.3.4 Bivariate Exponential 382

B.3.5 Chi-squared 383

B.3.6 Dirichlet 383

B.3.7 Exponential 386

B.3.8 Extreme Value 386

B.3.9 Gamma 389

B.3.10 Inverse Chi-squared 389

B.3.11 Inverse Gamma 392

B.3.12 Inverse Gaussian 392

B.3.13 Inverse Wishart 392

B.3.14 Logistic 396

B.3.15 Lognormal 396

B.3.16 Multinomial 399

B.3.17 Multivariate Normal 399

B.3.18 Negative Binomial 399

B.3.19 Negative Log-Gamma 401

B.3.20 Normal 403

B.3.21 Pareto 403

B.3.22 Poisson 403

B.3.23 Poly-Weibull 403

B.3.24 Student's t 406

B.3.25 Uniform 408

B.3.26 Weibull 408

B.3.27 Wishart 411

Reference 413

Author Index 427

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >